Magnetic Bearing with Radial Magnetized Permanent Magnets

Transcription

1 Wold Applied Sciences Jounal 23 (4): , 2013 ISSN IDOSI Publications, 2013 DOI: /idosi.wasj Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich Vavilov, Flu Rashitovich Ismagilov and Oksana Alexeevna oikova Ufa State Aviation Technical Univesity, Ufa, Russia Submitted: May 18, 2013; Accepted: Jun 15, 2013; Published: Jun 28, 2013 Abstact: The aticle eveals the elevance of magnetic beaings usage in high-speed electical complexes. Found that the use of high-coecive pemanent magnets in magnetic beaings allows to incease thei stength chaacteistics, eliability and to educe thei weight and size paametes The eseaches esults of the magnetic beaing on pemanent magnets ae given. The scheme fo detemining the magnetic beaings on pemanent magnets magnetic field patten is shown. Magnetic beaings on pemanent magnets pesented as the n-adialy magnetized pemanent magnets that allows to use it not only fo ing magnets magnetic field studies, but fo the secto magnets, which ae widely used as electic machines poles. The accepted assumptions fo detemination mathematical models given. The mathematical tool fo detemination the magnetic beaings on pemanent magnets thee-dimensional magnetic field paametes is developed. The simulation esults ae shown in the gaphs. The compaative analysis of expeimental data and compute modeling is given. The esults ae discussed. Key wods: High-speed electical complex Magnetic beaing Pemanent magnet Hybid magnetic beaing INTRODUCTION To solve this poblem it is necessay: In the moden industy the magnetic beaings find the To develop a mathematical model fo detemining the inceasing application in high-speed electical complexes, MPM magnetic induction at any point in space; because it allows to incease enegy efficiency, to To cay out numeical studies of the developed minimize themal losses and also to incease mathematical model and check its adequacy by envionmental fiendliness of such complexes. The use of compute simulation and expeimental studies. high-coecive pemanent magnets (the PM) in magnetic beaings (M) allows to incease thei stength Decision of Reseach Poblems: The scheme fo chaacteistics, eliability and to educe thei weight and detemining the MPM magnetic field patten is shown in size paametes [1, 2]. Figue 1. MPM pesented as the n-adially magnetized Magnetic beaing eseaches [3, 4] aimed at PM that allows to use it not only fo ing magnets detemining the ai gap stength chaacteistics, as they magnetic field studies, but fo the secto magnets, which ae the key indicatos of M seviceability. So, it is ae widely used as electic machines poles. necessay to detemine the patten distibution of M When developing mathematical model the following magnetic field. In [5] pesented expessions fo calculating assumptions wee accepted: the pemanent magnets magnetic field paametes of ectangula shape. ecause in M the cylindical PM ae pemanent magnets magnetic pemeability is constant used, so the expessions [5] may cause a significant eo. and equal to 1, which is typical fo the magnets fom In [6] the cylindical adial magnetized pemanent magnet NdFe; thee-dimensional magnetic field is consideed, but the the envionment magnetic pemeability is equal to awkwadness of solutions pesented limits its application vacuum magnetic pemeability; in pactice. So it s impotant to develop the mathematical tempeatue conditions ae invaiable thoughout tool that allows to detemine the magnetic beaings on MPM opeational pocess; pemanent magnets (MPM) thee-dimensional magnetic Magnetic field component in the y axis diection is field paametes. zeo because of the symmety. Coesponding Autho: D. Vavilov, Ufa State Aviation Technical Univesity, , Ufa, Kal Max Steet, 12, Republic of ashkotostan, Russia 495

2 Fig. 1: The scheme of the secto pemanent magnet (left) and the MPM (ight) The adial component of the PM magnetic induction The solution of expession (2) was made in the adial component, which, accoding to Coulomb's ule, fo pogam complex Mathcad, the following PM paametes any point in space can be defined as [5]: wee thus used: R 1= 28 mm, R 2= 25 mm, l = 6 mm, = 1 T. ( l 2 x) ( b 2) y ( l 2 x) ( b 2) y These paametes wee chosen due to the fact that they + z = actg + actg + coespond to the paametes used fo calculation in [6]. 4 2 z ( l 2 x) + ( b 2 y) + 2z 2 z ( l 2 x) + 2 y) + 2z The esults ae shown in Figue 2. ( l+ 2 x) ( b 2 y) ( l 2 x) 2 y) + actg + actg (1) The analysis of numeical modeling esults showed 2 z ( l+ 2 x) + ( b 2 y) + 2z 2 z ( l 2 x) + 2 y) + 2z thei convegence with the esults eceived on expessions, pesented in [6], the diffeence does not -PM esidual induction; x, y, z-coodinate point, exceed 2-3%. espectively, whee the magnetic induction is calculated; To detemine the adial component of magnetic field l-pm axial length; qr 1 1 (360 q2) R1-the length of in the MPM ai gap fist calculated the extenal magnetic b = pemanent magnet ach; R1-the adius of PM extenal cicle; q 1, q2-secto aches. The expession (1) does not take into account that the magnets in MPM and in hybid magnetic beaings (HM) have a cylindical shape and theefoe it will cause a significant eo, so it s necessay to take into account the cylindical fom of pemanent magnets. The adial component of magnetic induction at a distance, equal to (Figue 1), taking into account that coodinates of z, y ae cylindical, is defined as: q2 ( l 2 x) ( b 2ycos q) actg z q l x + b y q + z q q1 z = sin ( 2 ) ( 2 cos ) 2 sin ( l 2 x) 2ycos q) + actg + 2zsin q ( l 2 x) ( b 2 y) 2( zsin q) ( l + 2 x) ( b 2ycos q) + actg + 2zsin q ( l + 2 x) + ( b 2ycos q) + 2( zsin q) ( l 2 x) 2ycos q) + actg dq 2zsin q ( l 2 x) + 2ycos q) + 2( zsin q) the coodinate of z defined as. h z = + d 2 (2) induction adial component on the expessions simila to expession (2) then, with application of the magnetic fields supeposition pinciple the numeical calculations wee caied out. The esults ae pesented in figue 3. The analysis of the esults showed that at the minimum ai gap the magnetic induction adial component is minimum. The incease in the ai gap leads to incease in a adial component of a magnetic induction to the maximum value. Futhe incease in the ai gap educes the adial component of the magnetic induction. The maximum of the adial component ai gap induction, at the accepted numeical paametes, made 0,15 T, at a ai gap equal to 2 mm. ecause the adial component of foce is diectly popotional to z, the natue of the foce changes is simila to the natue of the changes in magnetic induction. This phenomenon was noted by the authos in [7]. Conside the axial component of the PM magnetic induction, which can be defined as: x = ln 4 (2 x+ l) + (2 y+ b) + 2 z (2 y + b) (2 x+ l) + (2 y b) + 2 z (2 y b) (2 x l) + (2 y b) + 2 z (2 y b) (2 x l) + (2 y+ b) + 2 z (2 y + b) (3) 496

3 Fig. 2: The change of PM magnetic induction adial component at change of the ai gap size Fig. 4: The dependence of the pemanent magnet magnetic induction axial component fom the ai gap size Fig. 5: The change of the magnetic induction axial Fig. 3: The change of the magnetic induction adial component in the MPM ai gap at change of the component in the MPM ai gap at change of the ai gap size ai gap size The analysis of the modeling esults showed that, The magnetic induction axial component at the similaly magnetic induction adial component, axial distance equal to (Figue 1), taking into account the component inceases with the incease in an ai gap fom cylindical coodinates of z, y is defined as: minimum, to the cetain value, calling theshold value of an ai gap, afte which it stats deceasing. Fo a studied q 2 (2 x+ l) + (2ycos q+ b) + 2( zsin q) (2ycos q+ b) case 2 is the theshold ai gap (0,28 T at the ai gap x = 4 (2 x+ l) + (2ycos q b) + 2( zsin q) (2ycos q b) equal to 2 mm). Impotantly, in the small gap, the gap to q1 (4) the theshold, the axial component of the magnetic (2 x l) + (2ycos q b) + 2( zsin q) (2ycos q b) dq induction of moe than 50-70% adial. In the egion of (2 x l) + (2ycos q+ b) + 2( zsin q) (2ycos q+ b) small ai gap, up to the size of a theshold ai gap, the axial component of a magnetic induction is 50-70% moe than Accoding to expession (4) numeical modeling the adial. So, in aea to theshold value of an ai gap the fo one magnet (Fig. 4) and fo the MPM ai gap pushing out axial foces ae moe than pushing away (Fig. 5) also was caied out. Analysis of the esults adial foces. Thus fo adial MPM axial foces ae showed thei convegence with the esults of [6], which paasitic (in a studied case). Fo checking the developed used a moe complex method. The diffeence does not mathematical expessions and fo confimation of the exceed 2-3%. eceived theoetical conclusions the compute modeling 497

4 Fig. 6: Installation fo PM magnetic field eseaches Fig. 7: Compaative analysis of the expeimental esults, the analytical and simulation of MPM powe chaacteistics in the pogam complex movement elative to the magnet 3. The amount of Ansys and MPM, consisting of two secto magnets movement is contolled by the indicato of hou type expeimental eseaches wee caied out. At compute ICH-8. modeling of thee-dimensional model bounday The Figue 7 shows the expeimental and analytical conditions to Diikhl wee used. When modeling the and compute simulation dependence of magnetic following PM paametes wee used: R1 = 30 mm, R2 = 60 induction adial and axial components on the change of mm, l = 6 mm, = 1,22 T, q1 = 0, q2 = /8. As a esult of the ai gap size/ modeling the values of magnetic field induction axial and 1-magnetic induction axial component: (analytical); 2- adial components wee eceived and wee compaed to magnetic induction axial component: (expeiment); 3- expeimental data and to numeical calculations of magnetic induction axial component: (modeling in Ansys); expessions (2),(4). 4-magnetic induction adial component: (analytical); 5- Expeimental eseaches wee caied out on the magnetic induction adial component: (expeiment); 6- authos' setup (Fig. 6). magnetic induction adial component: (modeling in Pesented in Figue 6 installation includes: 1-holdes, Ansys); in which ae set adial magnetized pemanent magnets 2, 3; the magnetic field measuing instument TPU-05 with a CONCLUSIONS set of feele gauges fo measuing the magnetic field adial and axial components 4; magnetic field measuing The esults analysis showed that the toe-out between instument feele gauge ests on the thust block 5, which analytical and expeimental data doesn't exceed 5% and ensues the accuacy on the coodinates x-axis; thust between the compute simulation and expeimental 2%- block 6 and pushe mechanism 7, poviding the magnet 2 3%. The obtained expeimental data confim theoetical 498

5 conclusions and theefoe, the developed mathematical 6. Swann, M.K., J. Watkins and K.R. onstein, models and esults of thei modeling can be used in Pesent limits of opeation of poduct lubicated and pactice at design of magnetic beaings on pemanent th magnetic beaings in pumps. Poceedings of the 14- magnets and hybid magnetic beaings. intenational Pump Uses Symposium, pp: REFERENCES 7. Ravaund, R., G. Lemaquand and V. Lemaquand, Foce and Stiffness of Passive Magnetic eaings Using Pemanent Magnets. Pat 1: Axial 1. Khayullin, I., F. Ismagilov and V. Vavilov, Magnetization. IEEE Tansctions on Magnetics, Hybid magnetic beaings stength detemination fo 45: 7. high-speed spindles. USATU messenge v., 16: Kasilnikov, A., The calculation of attaction 2. Geasin, A., F. Ismagilov and I. Khayullin, foces in high-coecive pemanent magnets in the Repulsive foce axial component analysis in a edge magnetic clutches and flat magnetic systems // multiing magnetic beaings with the axial diection of Jounal of Mechanical Engineeing. Numbe 6. the magnetization. uild in mechanical engineeing, 9. Ravaund, R., G. Lemaquand and V. Lemaquand, instument, 10: Analytical Calculation of the Magnetic 3. Johan, K., Femeey, Pemanentmagnetische Field Ceated by Pemanent-Magnet Rings. Lage: Jülich Foschungschungszentum Jülich. IEEE Tansctions on Magnetics 44: 8, august. 4. Jansen, R. and E. DiRusso, Passive Magnetic 10. Ismagilov, F., I. Khayullin and V. Vavilov, eaing with Feofluid Stabilization. NASA. NASA Magnetic beaings foce chaacteistics TM detemination, depending on the size of the woking 5. Johnson, D., P. Pillay and M. Malenget, ai gap / / USATU messenge, 16, # 8(53): High speed PM moto with hybid magnetic beaing fo kinetic enegy stoage. Confeence Recod-IAS Annual Meeting (IEEE Industy Applications Society), 1: